Performance Attribution in Financial Evaluation and Management

Getting Performance Attribution Andre Mirabelli, Ph.D. Opturo First Rate 2014 Performance Conference: Solutions through integration

A Clarifying Contextualization to The Nomenclature and Hierarchy Of Performance and Attribution: --------------------------------------------------- --------------------------------------------------- Performance systems: What inputs do they need & What questions can they answer? A. Mirabelli, of Opturo for First Rate 2014 2

Objective: Understanding the Explicit Evaluation Hierarchy forFinancial Measures and Their Defining Questions, With a special focus upon Ex-Post Attribution. A. Mirabelli, of Opturo for First Rate 2014 3

Will cover: Input Output Attribution A. Mirabelli, of Opturo for First Rate 2014 4

Input Kinds Periodicity Portfolio-level Issue-level Market Data Fund & Benchmark Specific Data A. Mirabelli, of Opturo for First Rate 2014 5

Input Specifics A. Mirabelli, of Opturo for First Rate 2014 6

Periodicity Not every moment. Too much data for ALL issues. Can settle up at close. But AT Priced Settlements ALL Fund & Benchmark A. Mirabelli, of Opturo for First Rate 2014 7

Portfolio-level Management Fees External flows A-temporals: Flows from not-now-owned. A. Mirabelli, of Opturo for First Rate 2014 8

Issue-level Market Data For all issues individually in Fund & Benchmark Corporate Actions Splits Accruals Dividends Coupons Interest Structural decompositions Drill-Downs (for ~swaps, ETFs ) A. Mirabelli, of Opturo for First Rate 2014 9

Descriptors/Categories Discrete or Continuous Currency/Country Sectors/Industries/Capitalizations Bond Ratings/Durations/Yields/Spreads Quant or Analyst Ratings Property- & Weight- tiles portfolio specific Take Averages, etc., for bifurcations A. Mirabelli, of Opturo for First Rate 2014 10

Fund & Benchmark Specific Data Prices (can differ) FX rates (can differ) Positions: Open Quantities Trades Quantities Prices Fees Time-stamps are superfluous A. Mirabelli, of Opturo for First Rate 2014 11

Outputs Returns & Weights at all levels Risk Measures at all levels Attribution to Uncontrollable market effects Controllable investment decisions A. Mirabelli, of Opturo for First Rate 2014 12

DEFINING QUESTIONS: A. Mirabelli, of Opturo for First Rate 2014 13

Ex-Anti: Predict the Future Given how the fund WILL be constructed, How WILL the market s evolution create the fund results? Snapshot Weights Project into Future Projectables: Exposures & Volatilities, Correlations, (Technicals) Projected/Predicted: Returns, Contributions, Risks Optimization of expectations APT, Barra, Northfield, Axioma, Rsquared, A. Mirabelli, of Opturo for First Rate 2014 14

Ex-Post: Evaluate the Past Why the past? Report card for Major Explain Past Fund Parameters in terms of: Uncontrollable Market Impacts Controllable Investment Decisions A. Mirabelli, of Opturo for First Rate 2014 15

Evaluate Fund parameters: Performance at all levels Basis = Amount Risked (W/ or W/O Lev) Gain = Market Change in Amount Risked W = Basis/(total Bases) R = Gain/Basis Contribution = Gain/(Total Open Value) Risks & Risk-Adjusted Returns Volatility, IR, A. Mirabelli, of Opturo for First Rate 2014 16

Weights, Returns & Fund BM/Tactical WBHj, WTrj Wj RBHj, RTrj Rj Category level Portfolio level Other Performance & Risk Measures A. Mirabelli, of Opturo for First Rate 2014 17

Uncontrollable Market Impacts Given how the fund was constructed, How did the market s evolution create the past fund results? If all Rj the same, there is no active return to explain. Thus, Market Diff Totally Explains. Victim Analysis: Results explained in terms of what the market did to the fund that was created. A. Mirabelli, of Opturo for First Rate 2014 18

Uncontrollable Market Impacts Market Explanations: Historic returns explained by Multi factor Market Attribution Deterministic Decomposition FIPA math intuition Market Differentiation Statistical Decomposition APT, Barra, Northfield, Axioma, Rsquared, Regress to find Exposures, Factors or both A. Mirabelli, of Opturo for First Rate 2014 19

Controllable Investment Decisions Given how the market evolved, How did the investment decisions create the fund results? If WTRj = WBMj there is no active R to explain. Thus, Decision Diff Totally Explains. Responsibility Analysis: Results explained in terms of the investment decisions that created the fund in the context of how the market evolved. A. Mirabelli, of Opturo for First Rate 2014 20

Decomposition Arbitrary Drill-down Brinson (BHB, BF) 2-step Single period/multi-period (smoothing) Karnosky-Singer (Investable Currency) 3-step Single period Menchero/Bertrand: IR A. Mirabelli, of Opturo for First Rate 2014 21

Economically meaningful: Impact of implementing a decision Decision Trees Multi-step & Bifurcation Multi-period exact w/ no smoothing Explain: R, G IRR (Internal Rate of Return) SD TE IR A. Mirabelli, of Opturo for First Rate 2014 22

For both Ex-Anti and Ex-Post Attribution, Modern Portfolio theory emphasizes that Explanations of Active returns without Explanations of Risk are dangerous. If you know a decision helped your returns but do not know how it affected your risk, your future decisions will be misdirected. A. Mirabelli, of Opturo for First Rate 2014 23

Take-Aways Needed data is usually available at some periodicity, but not always clean. Not all calculations of performance measures offered by providers are equally appropriate. Precise Math Meaningful measure Must begin with a clear question. Explanations in terms of Uncontrollable Market Results are very different in purpose and values from Explanations in terms of Controllable Investment Decisions. But, both need to explain both returns and risk. (MPT) A. Mirabelli, of Opturo for First Rate 2014 24